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March 10th, 2017, 12:02 AM   #1
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Stokes theorem

I am trying to figure out when and how to use Stokes theorem. I was looking at this video:



and I am really confused about how he uses the theorem. About 4.30 he writes down the integral using Stokes.

So if I am having a cylinder and some line integral around it. Then it doesn't matter how this line integral looks like? Seems like he is having some arbitrary line integral around that surface..

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March 10th, 2017, 03:50 AM   #2
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Stokes theorem works in the following way: Imagine you have a vector field $\vec{A}$, and you want to calculate the integral along a path $\gamma$ (in your case, this can be the integral along a line surrounding the cylinder). Then the following holds:

\begin{eqnarray}
\int_{\gamma}d\vec{s}.\vec{A}=\int_{S}d\vec{S}. \vec{\nabla}\times \vec{A}
\end{eqnarray}

where the integral on the right hand side is over the surface $S$, and $dS$ is the differential normal surface vector. This equality holds regardless of the geometry of the problem under consideration, so it is completely general. Hope it helps
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